They might care about other things, but greed is a near universal thing.Only if you presume your players literally never care about anything other than grabby-hands wealth-acquisition.
Sure the players can always just walk out of a game.1. There is absolutely a choice, the characters can say "royal vault, forget that - where going to do something else..." and not bother with the gold key.
Sure, but the flaw here is the DM presenting the three choices.2. Forgetting that, the players have only 1 choice ok. But let's say you present 3 different choices, but they actually all lead to the same place, no matter what the players actually do - that's railroading.
Not at all. In one, players are given the truth - "this is what you're doing if you want to follow the adventure...". In the other, railroading, the DM pretends there are multiple choices, but there really are not. The situation is not the same.
This is just really any time the players feel like complaining. Too many players feel the game world reality should just be altered at their whim. And when it does not happen: they cry railroad.Railroading occurs when you pretend that players can exercise choice, while actually denying them choice. That's it.
I agree: any random thing the players don't like or don't agree with and they will cry railroad.Hence, if the players get why you're doing this and (tacitly) agree it's legitimate, or if they're so swept up in the moment that it never occurs to them to do anything else, then cool. They're clearly on board this train, they aren't being railroaded, they're being transportedto where they want to go.
It's when the players don't actually agree and aren't actually swept up in it...but the DM uses tools like this to coerce their agreement out of them, no matter what...that we have a problem. And that can absolutely happen even if the DM only uses any particular tool once and only once per campaign.
The idea that the players should or must agree with the DM at all times is just silly.
Even for simple things. The characters find a bandit hideout, and the players have them run back to town. The "wacky player plan" is for the characters to go to the local arch mage and have them fix everything. When the characters do finally get to the mage tower though: they find the archmage is not home.
And right here is where many players will rant and rave about a Railroad. "The DM made the archmage not home as a personal attack on me!"